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受欢迎的三角函数 >

cos(2x)= 9/41

解答

cos (2 x) = \frac{9}{41}

解答

x = \frac{1.34948 \dots}{2} + πn, x = π - \frac{1.34948 \dots}{2} + πn

+1

度数

x = 38.65980 \dots^{\circ} + 18 0^{\circ} n, x = 141.34019 \dots^{\circ} + 18 0^{\circ} n

求解步骤

cos (2 x) = \frac{9}{41}

使用反三角函数性质

cos (2 x) = \frac{9}{41}

cos (2 x) = \frac{9}{41}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 x = arccos (\frac{9}{41}) + 2 πn, 2 x = 2 π - arccos (\frac{9}{41}) + 2 πn

2 x = arccos (\frac{9}{41}) + 2 πn, 2 x = 2 π - arccos (\frac{9}{41}) + 2 πn

解

2 x = arccos (\frac{9}{41}) + 2 πn : x = \frac{arccos ( \frac{9}{41} )}{2} + πn

2 x = arccos (\frac{9}{41}) + 2 πn

两边除以

2

2 x = arccos (\frac{9}{41}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{9}{41} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{9}{41} )}{2} + πn

x = \frac{arccos ( \frac{9}{41} )}{2} + πn

解

2 x = 2 π - arccos (\frac{9}{41}) + 2 πn : x = π - \frac{arccos ( \frac{9}{41} )}{2} + πn

2 x = 2 π - arccos (\frac{9}{41}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{9}{41}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{9}{41} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{9}{41} )}{2} + πn

x = π - \frac{arccos ( \frac{9}{41} )}{2} + πn

x = \frac{arccos ( \frac{9}{41} )}{2} + πn, x = π - \frac{arccos ( \frac{9}{41} )}{2} + πn

以小数形式表示解

x = \frac{1.34948 \dots}{2} + πn, x = π - \frac{1.34948 \dots}{2} + πn

作图

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